The sample is a subset of the whole population selected to be questioned for the purposes of prediction or gauging opinion .
A sample is a collection of people, things, or things used in research that is taken for analysis from a larger population. To enable us to extrapolate the research sample's findings to the entire population, the sample must be representative of the population.
We must utilize inferential statistics to discover a population's characteristics by directly observing only a subset (or sample of the population) in order to derive conclusions about populations from samples.
Since it is frequently impractical and hardly ever possible, we acquire a sample of the population.
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what is the sum of the exponents of the prime factors of the square root of the largestperfect square that divides 12! ?
8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
We are asked the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!.
As, the largest perfect square that divides 12! is
2^10 * 3^4 *5^2 = 2073600.
Now, the square root of the number 2073600 is,
1440
Now, we have to find the prime factorization of 1440
1440 = 2×2×2×2×2×3×3×5
Now, in the prime factorization of 1440
the exponent of 2 is 5, exponent of 3 is 2 and the exponent of 5 is 1.
So, the sum of the exponents of the prime factors be 5+2+1 = 8
Hence, 8 is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides 12!
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Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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Decrease 330 km by 54%.
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
Solve for X please help
Answer:
17
Step-by-step explanation:
4x-10=58(alternate interior angles)
4x=68
x=17
The ordered pairs show the number of hours a student studied in a week, x, and that student’s exam score, y.
(1,70) (3,75) (5,80) (9,95) (12,98)
The equation y=2.7x+67 can be used to model the relationship between the number of hours a student studied in a week and their exam scores. Choose a number from each box to make the statement true.
The y-intercept shows that a student who studies____________
A: 0
B: 2.7
C: 67
D: 69.7
hours can expect to get a score of _______on the exam.
A: 0
B: 2.7
C: 67
D: 69.7
Answers:
1st box: 0
2nd box: 67
===============================================
Explanation:
The y intercept always occurs when x = 0. This is when the function curve either crosses or touches the vertical y axis. Therefore, the y intercept is when the student studies 0 hours
Plug x = 0 into the equation
y = 2.7x + 67
y = 2.7*0 + 67
y = 67
Or you can note that the equation is of the form y = mx+b
m = slope = 2.7b = 67 = y interceptThe y-intercept of 67 tells us that the person studying for 0 hours is estimated to get a score of 67
A sample of size 50 from a normal distribution has sample mean 5 and sample variance 20. Find 96% confidence intervals for the variance and standard deviation of the distribution.
The standard deviation and variance of the distribution's 96% confidence intervals are 9.841 and 5.704, respectively.
A normal distribution sample of size 50 has an expected higher rate of 20 and a sample mean of 5.
n = 50 makes up the sample size.
Furthermore, the sample variance is s² = 20
The following is the formula for both the variance confidence interval:
σ² = [tex](\frac{(n-1)s^2}{X^2_{{n-1};{1-\alpha /2}}}, \frac{(n-1)s^2}{X^2_{{n-1};{\alpha/2}}})[/tex]
Here, [tex]{X^2_{{n-1};{1-\alpha /2}}}[/tex] is the critical value at the status of significance [tex]\alpha[/tex] & degree of freedom n - 1.
The 90% confidence interval's lower bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (30.114)
= 32.54
The 90% confidence interval's upper bound for variance is stated as,
[tex]\frac{(n-1)s^2}{ {X^2_{{49};{0.95}}}}[/tex] = (49 × 20) ÷ (10.117)
= 96.86
Consequently, the confidence level for the distribution's variance is (96.86, 32.54).
Additionally, the range of the distribution's standard deviation inside the 90% confidence interval is (√96.86, √32.54), that's the same as (9.841, 5.704).
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The perimeter of this triangle is not more than 30 cm. 2n+3 cm, 2n+2 cm, n cm
a. Write an inequality to show this.
b. Solve the inequality.
c. What are the largest possible lengths of the sides?
The inequality to represent the perimeter of the triangle is given by (2n + 3) + (2n + 2) + n ≤ 30
The solution to the inequality is n ≤ 5 The largest possible lengths of the sides is 13 cmInequality to represent the perimeter of a trianglePerimeter of the triangle = not more than 30 cmSide a = (2n + 3)cmSide b = (2n + 2) cmSide c = n cmSide a + side b + side c ≤ perimeter of the triangle
(2n + 3) + (2n + 2) + n ≤ 30
open parenthesis2n + 3 + 2n + 2 + n ≤ 30
5n + 5 ≤ 30
substract 5 from both sides
5n ≤ 30 - 5
5n ≤ 25
divide both sides by 5n ≤ 25/5
n ≤ 5 cm
The largest possible lengths of the sides is:
Side a = (2n + 3)cm
= 2(5) + 3
= 10 + 3
= 13 cm
Side b = (2n + 2) cm
= 2(5) + 2
= 10 + 2
= 12 cm
Side c = n cm
= 5 cm
So therefore, the largest possible length of the triangle is 13 cm
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations that can be used to solve for y, the length of the room
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0How do we obtain the relevant equations that can be used for the problem?First and foremost, we can begin solving this equation by noting the formula for calculating the area of a rectangle. This formula is given as follows:
Area of a rectangle = Length × Width
Since the width of the room is 5 feet less than the length of the room, we will have the resulting equation as the area of the rectangle:
y( y - 5) = 750
When this equation is fully expressed, we will get the following equations:
y2 – 5y = 750 750 – y(y – 5) = 0 (y + 25)(y – 30) = 0Therefore, options, B, C, and E are correct.
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Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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Solve for a side in right triangles
Really need help with this one!!
The value of side AC is AC = 3.
What is right triangle?
A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.
The given triangle ΔABC is a right angled triangle.
So, to find the side AC we can use the cosine ratio,
[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]
AC ≈ 3.
Hence, the length of side AC is 3.
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In a two-digit number, the unit digit is 5 more than the tens digit. The number itself is three times the sum of the digits. What is the number?
Answer:
27
Step-by-step explanation:
You want a 2-digit number that is 3 times the sum of its digits, where the units digit is 5 more than the tens digit.
SetupLet t represent the tens digit. Then the units digit is (t+5) and the sum of digits is ...
t +(t +5) = 2t+5
The value of the number is ...
10t +(t+5) = 11t +5
The value is 3 times the sum of digits, so we have ...
11t +5 = 3(2t +5)
Solution11t +5 = 6t +15
5t = 10 . . . . . . . . . . subtract (6t+5)
t = 2
(t+5) = 7
The number is 27.
You have 7,160 grams of a radioactive kind of bismuth. How much will be left after 10 days if
its half-life is 5 days?
grams
The solution is 1790 grams
The amount of bismuth left after 10 days if the half life is 5 days will be
1790 grams
What is half-life of an element?
The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the half life of the element be represented as t½
The value of t½ = 5 days
Now , the initial amount of bismuth N₀ = 7160 grams
The number of days t = 10 days
The amount of bismuth left after 10 days = N( t )
Now , the value of N( t ) is given by the formula ,
N( t ) = N₀ ( 1/2 )^ t/ t½
Substituting the values in the equation , we get
N( t ) = 7160 ( 1/2 )^10/5
N( t ) = 7160 ( 1/2 )²
N( t ) = 7160 / 4
N( t ) = 1790 grams
Therefore , the value of N( t ) is 1790 grams
Hence , the amount of bismuth left is 1790 grams
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7. The total cost of Mrs. Goodwin's donut purchase varies directly with the amount of donuts purchased. If
the total cost was $7.50 for 15 donuts, how many donuts can she purchase for $10.00?
The number of donuts that can be purchased for $10 is 20.
The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.
Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.
The price is directly proportional to the number of donuts purchased.
p ∝ n
We will remove the proportionality sign.
p = k*n
7.5 = k*15
k = 1/2
The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.
p = (1/2)n
10 = (1/2)n
n = 10*2
n = 20
Hence, the number of donuts that can be purchased for $10 is 20.
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Please help
The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?
6 feet
2.7 feet
8 feet
3 feet
The value of their horizontal change is 2.7 feet
How to determine the value of their horizontal change?The equation of the function is given as
y = -8/3x + 40
From the question, the distance travelled by the rider is given as
Distance = 8 feet downward
This means that
Horizontal change = slope
A linear equation is represented as
y = mx + c
Where
Slope = m
By comparing y = mx + c and y = -8/3x + 40, we have
Slope = m = 8/3
This gives
Horizontal change = 8/3
Evaluate
Horizontal change = 2.7
Hence, the horizontal change is 2.7 feet
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2x-84=108
x=?
please help
Answer:
X=
Step-by-step explanation:
Let's solve your equation step-by-step.
2x−84=108x
Step 1: Subtract 108x from both sides.
2x−84−108x=108x−108x
−106x−84=0
Step 2: Add 84 to both sides.
−106x−84+84=0+84
−106x=84
Step 3: Divide both sides by -106.
−106x
−106
=
84/−106x=−42/53
simplify 1/x^-5 HELP ME PLEASE FIRST ANSWER GETS BRAINLIEST
Answer:
x^5
Step-by-step explanation:
: the small town of west fremont has a population of 50,000. if the growth rate of west fremont is 2%, then how long will it take for the population of west fremont to double?
It takes 35 years for the population of West Fremont to double. We have the following condition;
West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.
Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.
According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.
Doubling time = 70 / Growth rate
= 70 / 2
= 35 years
So, it takes 35 years for the population of West Fremont to double.
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how many cubes are added
The number of centimeter cubes to be added to make the cuboid is; 30 cubes.
How to Interpret the elevation of objects?From the given plan, side elevation and front elevation, we can see that the number of cubes needed to make the shape is 18 blocks.
From the front elevation, 12 blocks is required (4 * 3 blocks).
From the side elevation, 6 blocks are required which gives us a total of 18 blocks.
The number of blocks needed to make the given cuboid is;
Volume of cuboid = 4 * 4 * 3 = 48 cm cubes.
Therefore the number of cubes to be added = Volume cubes - Number of cubes from elevation
The number of cubes to be added = 48 cubes - 18 cubes
The number of cubes to be added = 30 cubes.
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HELP ME PLEASEEEEEEE
Answer:
[tex]{ \boxed{ \tt{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}[/tex]
- \theta = 25°
- opposite = x
- hypotenuse = z
[tex]{ \tt{ \sin(25 \degree) = \frac{x}{z} }} \\ [/tex]
Answer: x/z
Step-by-step explanation:
sin25 uses soh from sohcahtoa
sin25 = opposite/hypotenuse = x/z
Can anyone write the equation of the graph?
NEED HELP FINDING THE EQUATION!!! THXXXX
Answer:
See below
Step-by-step explanation:
Horizontal lines have ZERO slope
Vertical lines have 'undefined' slope
for this example x = 1/2 includes the point and has undiefined slope
Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg
Answer:
4/7
Step-by-step explanation:
32:56
32÷2=16
56÷2=28
16:28
16÷2=8
28÷2=14
8:14
8÷2=4
14÷2=7
4:7
32:56 ~ 32/56
=4/7
bob can do a job in 5 hours while bill can do the same job in 8 hours. how many hours would it take them, working together, to do this job?
Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
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cheyenne needs to cut a piece of paper so that she has exactly 1/3 of it. if the length of the paper is 11 inches, how long will be the piece that she cuts?
The lengths of the piece she should cut is = 3 2/3
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
1/3 of 11=1/3*11=11/3=3 2/3hence,The lengths of the piece she should cut is = 3 2/3
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Given: AD
Prove: DE
A
D
BC and ZBCD ZADC
CE
C
Intro
B
Correct! Assemble the next
statement.
Angles Segments Triangles Statements Reasons
SAS
CPCTC
reflexive property
Statements
✓1. AD BC
✓ 2. ZDEA and CEB are
vertical angles
3. ZBCD
ZADC
vertical angles theorem
Reasons
1. given
2. def. of vertical angles
3. given
Triangle ADC and ΔBDC are congruent. then DE ≅ CE
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same form and size.Given,
AD ≅ BC
∠BCD ≅ ∠ADC
In triangle ADC and ΔBDC
AD ≅ BC ( GIVEN )
∠BCD ≅ ∠ADC ( GIVEN )
DC = DC ( Common line)
so triangle ADC and ΔBDC are congruent.
then DE ≅ CE
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a data analyst creates a scatterplot. the analyst wants to put a text label on the plot to call out specific data points. what function does the analyst use?
The analyst should use the alpha aesthetic. The alpha aesthetic makes some points on a plot more transparent than others to call out specific data points.
What is scatterplot?A set of points plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of correlation, if any, between the values of observed quantities or phenomena, scatter plots are crucial in statistics (called variables). In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.
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help meeeeeeeeeee pleaseeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
The dive lasted approximately [tex] \boxed{\sf 2.76} [/tex] seconds.
Step-by-step explanation:
Given formula: h = 16t²
Where, t is time in seconds and h is the distance in feet traveled by a free-falling body or object.
According to the question,
Height of the cliff from which diver dives (h) = 122 feet.
By substituting the value of height in the formula we get:
[tex]\rm \implies 122 = 16 {t}^{2} \\ \\ \rm \implies {t}^{2} = \dfrac{122}{16} \\ \\\rm \implies {t}^{2} = 7.625 \\ \\ \rm \implies t = \sqrt{7.625} \\ \\ \rm \implies t = 2.76 \: seconds[/tex]
Can someone help me with this aleks question
For the given triangles ΔTRS and ΔQRP , the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
As given in the question,
Two triangles ΔTRS and ΔQRP,
It is given that :
Line segment SR ≅ Line segment PR
Line segment SP bisects Line segment TQ
⇒ line segment TR ≅ line segment RQ
∠TRS ≅ ∠PRQ ( by vertically opposite angle )
By Side angle side theorem we have ,
ΔTRS ≅ ΔPRQ
Therefore, for the given triangles ΔTRS and ΔQRP ,the required step to prove both the triangles are congruent is ∠TRS ≅ ∠QRP.
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avoiding an accident when driving can depend on reaction time. that time, measured from the moment a driver sees the danger until he/she gets his/her foot on the brake pedal, is normally distributed with a mean of 1.5 seconds and a standard deviation of 0.18 seconds. what is the interquartile range of the reaction times? report your answer to at least the nearest hundredth of a second (i.e. with at least two digits after the decimal point).
The interquartile range of the reaction times is 0.528 or 52.80%
A normal model is represented as (μ, σ). Therefore for (1.5, 0.18), the mean (μ) = 1.5 and the standard deviation (σ) = 0.18
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
The z score shows by how many standard deviations the raw score is above or below the mean. It is given as:
The interquartile range is x = 1.45 and x = 1.75
For x = 1.45
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Z=(1.45-1.5)/0.18
= -0.28
For x = 1.75
Z=(1.75-1.5)/0.18
= -1.39
From the normal distribution table,
P(1.45 < x < 1.75) = P(-0.28 < z < 1.39)
= P(z < 1.39) - P(z< - 0.28)
= 0.9177 - 0.3897
= 0.528
= 52.8%
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